Negative binomial multiplicity distributions for proton-nucleus collisions from a string model

Abstract

Multiplicity distributions of charged particles produced in collisions of ultrarelativistic protons with nuclei are studied in a string model. Recently measured multiplicity distributions in proton-nucleus reactions display a negative binomial shape. The string model VENUS reproduces the data well. We trace back within the model the origin of the negative binomial form of the multiplicity distributions. We find that the final multiplicity distribution can be expressed as a continuous superposition of Poisson distributions with different mean multiplicities ∫dNW(N)P(N, n). The Poisson distribution represents the string fragmentation, whereas the weight factorW(N) reflects the string mass distribution. This quantity has contributions due to both the nuclear structure and the parton structure of nucleons. We show thatW(N) is very well approximated by a gamma-distribution . This leads to a negative binomial distribution\(\mathcal{N}(k,\bar N;n)\) with the same parameters as for . It is shown that the fluctuations in the multiplicity are dominated by the string fragmentation fluctuations for small rapidity intervals and by string mass and number fluctuations for large rapidity windows.